Analytical solution to a time-varying LIP model for quadrupedal walking on a vertically oscillating surface

Hutter M, Gehring C, Jud D, Lauber A, Bellicoso CD, Tsounis V, et al. ANYmal-a highly mobile and dynamic quadrupedal robot. In: Proc. IEEE/RSJ Int. Conf. Intel. Rob. Syst.. 2016, p. 38–44. Fawcett, 2021, Robust stabilization of periodic gaits for quadrupedal locomotion via QP-based virtual constraint controllers, IEEE Contr. Syst. L., 6, 1736, 10.1109/LCSYS.2021.3133198 Mastalli, 2020, Motion planning for quadrupedal locomotion: Coupled planning, terrain mapping, and whole-body control, IEEE Trans. Rob., 36, 1635, 10.1109/TRO.2020.3003464 Gu, 2018, Exponential stabilization of fully actuated planar bipedal robotic walking with global position tracking capabilities, ASME J. Dyn. Syst. Meas. Contr., 140, 10.1115/1.4038268 Gao Y, Gu Y. Global-position tracking control of multi-domain planar bipedal robotic walking. In: Proc. ASME Dyn. Sys. Contr. Conf.. 2019, p. V001T03A009. Xu, 2020, Adaptive impedance control with variable target stiffness for wheel-legged robot on complex unknown terrain, Mechatron., 69, 10.1016/j.mechatronics.2020.102388 Iqbal, 2020, Provably stabilizing controllers for quadrupedal robot locomotion on dynamic rigid platforms, IEEE/ASME Trans. Mechatron., 25, 2035, 10.1109/TMECH.2020.2999900 Gao Y, Yuan C, Gu Y. Invariant Extended Kalman Filtering for Hybrid Models of Bipedal Robot Walking. In: Proc. IFAC Mod. Est. Contr. Conf, vol. 54, no. 20. 2021, p. 290–7. Shih, 2012, From stable walking to steering of a 3D bipedal robot with passive point feet, Rob., 30, 1119 Motahar MS, Veer S, Poulakakis I. Composing limit cycles for motion planning of 3D bipedal walkers. In: Proc. IEEE Conf. Dec. Contr.. 2016, p. 6368–74. Gao Y, Gu Y. Global-position tracking control of a fully actuated NAO bipedal walking robot. In: Proc. Amer. Contr. Conf.. 2019, p. 4596–601. Gao, 2022, Invariant filtering for legged humanoid locomotion on dynamic rigid surfaces, IEEE/ASME Trans. Mechatron., 27, 1900, 10.1109/TMECH.2022.3176015 Chen Y-M, Posa M. Optimal reduced-order modeling of bipedal locomotion. In: Proc. Int. Conf. Rob. Autom.. 2020, p. 8753–60. Kajita S, Kanehiro F, Kaneko K, Yokoi K, Hirukawa H. The 3D linear inverted pendulum mode: A simple modeling for a biped walking pattern generation. In: Proc. IEEE Int. Conf. Intel. Rob. Syst. vol. 1. 2001, p. 239–46. Caron, 2019, Capturability-based pattern generation for walking with variable height, IEEE Trans. Rob., 36, 517, 10.1109/TRO.2019.2923971 Xiong, 2022, 3-D underactuated bipedal walking via H-LIP based gait synthesis and stepping stabilization, IEEE Trans. Rob., 38, 2405, 10.1109/TRO.2022.3150219 Gong, 2022, Zero dynamics, pendulum models, and angular momentum in feedback control of bipedal locomotion, ASME J. Dyn. Syst. Meas. Contr., 144, 10.1115/1.4055770 Westervelt, 2007 Pratt J, Carff J, Drakunov S, Goswami A. Capture point: A step toward humanoid push recovery. In: Proc. IEEE Int. Conf. Humanoid Rob.. 2006, p. 200–7. Mihalec, 2020, Recoverability estimation and control for an inverted pendulum walker model under foot slip, 771 Zhao, 2017, Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model, Int. J. Rob. Res., 36, 1211, 10.1177/0278364917730602 Li, 2020, Centroidal-momentum-based trajectory generation for legged locomotion, Mechatron., 68, 10.1016/j.mechatronics.2020.102364 Kimura, 2021, Extended balance stabilization control for humanoid robot on rotational slope based on seesaw-inverted-pendulum model, Adv. Rob., 35, 1116, 10.1080/01691864.2021.1959398 Dai, 2022 Zheng Y, Yamane K. Ball walker: A case study of humanoid robot locomotion in non-stationary environments. In: Proc. IEEE Int. Conf. Rob. Autom.. 2011, p. 2021–8. Yang C, Zhang B, Zeng J, Agrawal A, Sreenath K. Dynamic Legged Manipulation of a Ball Through Multi-Contact Optimization. In: Proc. IEEE Int. Conf. Intel. Rob. Syst.. 2020, p. 7513–20. Asano F. Modeling and Control of Stable Limit Cycle Walking on Floating Island. In: Proc. IEEE Int. Conf. Mechatron.. 2021, p. 1–6. Iqbal, 2021, Modeling, analysis, and control of SLIP running on dynamic platforms, ASME L. Dyn. Syst. Contr., 1 Kapitza, 1951, Dynamic stability of a pendulum with an oscillating point of support, Zh. Eksp. Teor. Fiz., 21, 588 Tannuri, 2003, Estimating directional wave spectrum based on stationary ship motion measurements, App. Ocean Res., 25, 243, 10.1016/j.apor.2004.01.003 Kajita S, Kanehiro F, Kaneko K, Fujiwara K, Harada K, Yokoi K, et al. Biped walking pattern generation by using preview control of zero-moment point. In: Proc. IEEE Int. Conf. Rob. Autom. vol. 2. 2003, p. 1620–6. Paredes VC, Hereid A. Resolved motion control for 3d underactuated bipedal walking using linear inverted pendulum dynamics and neural adaptation. In: Proc. IEEE Int. Conf. Int. Rob. Sys.. 2022, p. 6761–7. Iqbal A, Gu Y. Extended Capture Point and Optimization-based Control for Quadrupedal Robot Walking on Dynamic Rigid Surfaces. In: Proc. IFAC Mod. Est. Contr. Conf. vol. 54, no. 20. 2021, p. 72–7. Yoon, 2008, Development of the motion monitoring system of a ship, J. Navig. Port. Res., 32, 15, 10.5394/KINPR.2008.32.1.015 Gahlinger, 2000, Cabin location and the likelihood of motion sickness in cruise ship passengers, J. Trav. Med., 7, 120, 10.2310/7060.2000.00042 Benjamin, 1954, The stability of the plane free surface of a liquid in vertical periodic motion, Proc. R. Soc. London, 225, 505 Farkas, 2013 Phelps III, 1965, An analytical solution of the inverted pendulum, Amer. J. Phys., 33, 285, 10.1119/1.1971474 Werth, 2005, Charged particle traps: Physics and techniques of charged particle field confinement Bateman, 1953 Dougall, 1915, The solution of Mathteu’s differential equation, Proc. Edinb. Math. Soc., 34, 176, 10.1017/S0013091500037561 Floquet, 1883, Sur les équations différentielles linéaires à coefficients périodiques, 47 Gu, 2022, Global-position tracking control for three-dimensional bipedal robots via virtual constraint design and multiple Lyapunov analysis, ASME J. Dyn. Syst. Meas. Contr., 144, 10.1115/1.4054732 Winkler, 2018, Gait and trajectory optimization for legged systems through phase-based end-effector parameterization, IEEE Rob. Autom. L., 3, 1560, 10.1109/LRA.2018.2798285 Xin S, Orsolino R, Tsagarakis N. Online relative footstep optimization for legged robots dynamic walking using discrete-time model predictive control. In: Proc. IEEE/RSJ Int. Conf. Intel. Rob. Syst.. 2019, p. 513–20. Wächter, 2006, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Prog., 106, 25, 10.1007/s10107-004-0559-y Grizzle, 2001, Asymptotically stable walking for biped robots: Analysis via systems with impulse effects, IEEE Trans. Autom. Contr., 46, 51, 10.1109/9.898695 Iqbal A, Veer S, Gu Y. Asymptotic stabilization of aperiodic trajectories of a hybrid-linear inverted pendulum walking on a vertically moving surface. In: Proc. Amer. Contr. Conf.. 2023, p. 3030–5. Gao, 2022, Exponential stabilization of periodic LIP walking on a horizontally moving surface, Proc. Dyn. Walk. Conf. Gao Y, Gong Y, Paredes V, Hereid A, Gu Y. Time-Varying ALIP Model and Robust Foot-Placement Control for Underactuated Bipedal Robotic Walking on a Swaying Rigid Surface. In: Proc. Amer. Contr. Conf.. 2023, p. 3282–7. Bledt G, Powell MJ, Katz B, Di Carlo J, Wensing PM, Kim S. MIT Cheetah 3: Design and control of a robust, dynamic quadruped robot. In: Proc. IEEE/RSJ Int. Conf. Intel. Rob. Syst.. 2018, p. 2245–52.